TY - JOUR A1 - Grimm, Veronika A1 - Kleinert, Thomas A1 - Liers, Frauke A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Optimal Price Zones of Electricity Markets: A Mixed-Integer Multilevel Model and Global Solution Approaches JF - Optimization Methods and Software N2 - Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design yields welfare-optimal outcomes. This problem leads to a challenging multilevel model that contains a graph-partitioning problem with multi-commodity flow connectivity constraints and nonlinearities due to proper economic modeling. Furthermore, it has highly symmetric solutions. We develop different problem-tailored solution approaches. In particular, we present an extended KKT transformation approach as well as a generalized Benders approach that both yield globally optimal solutions. These methods, enhanced with techniques such as symmetry breaking and primal heuristics, are evaluated in detail on academic as well as on realistic instances. It turns out that our approaches lead to effective solution methods for the difficult optimization tasks presented here, where the problem-specific generalized Benders approach performs considerably better than the methods based on KKT transformation. KW - Multilevel Optimization KW - Mixed-Integer Nonlinear Optimization KW - Graph Partitioning KW - Generalized Benders Decomposition KW - Electricity Market Design} Y1 - 2017 IS - 34(2) SP - 406 EP - 436 ER - TY - JOUR A1 - Ambrosius, Mirjam A1 - Grimm, Veronika A1 - Kleinert, Thomas A1 - Liers, Frauke A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization with Graph Partitioning JF - Energy Economics N2 - In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the optimal configuration of price zones and available transfer capacities on a network in order to optimally govern investment and production decisions in the long run. In a multilevel mixed-integer nonlinear model that contains a graph partitioning problem on the first level, we determine welfare-maximizing price zones and available transfer capacities for a given electricity market and analyze their impact on market outcomes. Using a generalized Benders decomposition approach developed in Grimm et al. (2019) and a problem-tailored scenario clustering for reducing the input data size, we are able to solve the model to global optimality even for large instances. We apply the approach to the German electricity market as an example to examine the impact of optimal zoning on key performance indicators such as welfare, generation mix and locations, or electricity prices. It turns out that even for a small number of price zones, an optimal configuration of zones induces a welfare level that almost approaches the first best. KW - Electricity Markets KW - Price Zones KW - Investment Incentives KW - Multilevel Optimization KW - Graph Partitioning Y1 - 2018 IS - 92 ER -